Quantifying formidable multiple coupling effects involved in Surface-enhanced Raman scattering (SERS) is a prerequisite for accurate design of SERS probes with superior detection limit and uniformity which are the targets for trace substance detection. Here, combining theory and experiments on novel 3D periodic Au/SiO2 hybrid nanogrids, we successfully develop a generalized methodology of accurately designing high performance SERS probes. Structural parameters and symmetry, Au roughness, and polarization are quantitatively correlated to intrinsic electromagnetic field (EMF) enhancements from surface plasmon polariton (SPP), localized surface plasmon resonance (LSPR), optical standing wave and their couplings theoretically, which is experimentally verified. The hexagonal SERS probes optimized by the methodology successfully detect 5*10^-11 M Hg ions in water, and 2.5*10^-11 M R6G with 40 times improvement of detection limit, an enhancement factor of 3.4*10^8 and uniformity of 5.56%, which results from the extra Au roughness - independent 144% contribution of LSPR effects excited by SPP interference waves as secondary sources, beyond the conventional recognization. This study opens up a pioneering way not only for providing the generalized design principles of SERS probe structures with high performance but for accurately designing their structures with particular purposes such as greatly improved detection limit and uniformity which are very significant for trace substance detection.
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